39 lines
1.8 KiB
Markdown
39 lines
1.8 KiB
Markdown
# Introduction
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The unit circle has a center a $(0, 0)$, and a radius of $1$ with no defined unit.
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Sine and cosine can be used to find the coordinates of specific points on the unit circle.
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**Sine likes $y$, and cosine likes $x$.**
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When sine is positive, the $y$ value is positive. When $x$ is positive, the cosine is positive.
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$$ cos(\theta) = x $$
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$$ sin(\theta) = y $$
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## Sine and Cosine
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| Angle | $0$ | $\frac{\pi}{6}$ or $30 \degree$ | $\frac{\pi}{4}$ or $45\degree$ | $\frac{\pi}{2}$ or $90\degree$ |
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| ------ | --- | ------------------------------- | ------------------------------ | ------------------------------ |
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| Cosine | 1 | $\frac{\sqrt{3}}{2}$ | $\frac{\sqrt{2}}{2}$ | $0$ |
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| Sine | 0 | $\frac{1}{2}$ | $\frac{\sqrt{2}}{2}$ | <br>$1$ |
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Finding a reference angle:
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| Quadrant | Formula |
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| -------- | --------------------- |
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| 1 | $\theta$ |
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| 2 | $180\degree - \theta$ |
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| 3 | $\theta - 180\degree$ |
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| 4 | $360\degree - \theta$ |
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## The Pythagorean Identity
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The Pythagorean identity expresses the Pythagorean theorem in terms of trigonometric functions. It's a basic relation between the sine and cosine functions.
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$$ sin^2 \theta + cos^2 \theta = 1 $$
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# Definitions
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| Term | Description |
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| ---------------- | ----------------------------------------------------------------------------- |
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| $\theta$ (theta) | Theta refers to the angle measure in a unit circle. |
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| $s$ | $s$ is used to the length of the arc created by angle $\theta$ on the circle. | |